Time-Domain Adaptive Harmonic Control for Sinusoidal Disturbances Rejection

We present two time-domain feedback control algorithms for rejection of known-frequency sinusoidal disturbances that act on an asymptotically stable linear time-invariant (LTI) system. The first algorithm is time-domain harmonic control (TDHC), which is effective for uncertain LTI systems. However, TDHC requires an estimate of the control-to-performance transfer function evaluated at the disturbance frequency. The second algorithm is time-domain adaptive harmonic control (TDAHC), which is effective for completely unknown LTI systems. We analyze the stability and performance of TDHC and TDAHC for the case where there is a single performance measurement. For both TDHC and TDAHC, we show that the controller asymptotically rejects the disturbance. We also present numerical simulations comparing TDHC and TDAHC with higher-harmonic control, which is an existing sinusoidal disturbance rejection method.